Efficient topological compilation for a weakly integral anyonic model
Alex Bocharov, Shawn Xingshan Cui, Vadym Kliuchnikov, Zhenghan Wang · Physical Review A · 2016
A class of anyonic models for universal quantum computation based on weakly-integral anyons has been recently proposed. While universal set of gates cannot be obtained in this context by anyon braiding alone, designing a certain type of sector charge measurement provides universality. In this paper we develop a compilation algorithm to approximate arbitrary $n$-qutrit unitaries with asymptotically efficient circuits over the metaplectic anyon model. One flavor of our algorithm produces efficient circuits with upper complexity bound asymptotically in $O({3}^{2\phantom{\rule{0.16em}{0ex}}n}\phantom{\rule{0.16em}{0ex}}log1/\ensuremath{\varepsilon})$ and entanglement cost that is exponential in $n$. Another flavor of the algorithm produces efficient circuits with upper complexity bound in $O(n\phantom{\rule{0.16em}{0ex}}{3}^{2\phantom{\rule{0.16em}{0ex}}n}\phantom{\rule{0.16em}{0ex}}log1/\ensuremath{\varepsilon})$ and no additional entanglement cost.